Sevilla equalised early in the second period after battling their way back into the contest, but Alcacer's second of the night in the 65th minute proved the difference on a rainy evening in Barcelona.
The result means that the league leaders have again moved four points clear of second-placed Valencia, while the Catalan giants are now 11 points clear of fourth-placed Real Madrid.
The big team news in the Barcelona camp saw Alcacer start just his second La Liga match of the season, while Ivan Rakitic and Gerard Pique both returned to the XI following the Olympiacos clash during the week.
Barcelona had three opportunities to score inside the opening five minutes of action, but Soria did well to keep out a strike from Messi, before Sergio Busquets had a close-range effort cleared off the line.
Luis Suarez also had a super chance for the home side after breaking into a one-on-one situation with Soria, but the Uruguay international could not chip his effort over the onrushing Sevilla goalkeeper. Rakitic was next to come close in the seventh minute, with the Croatian's long-range strike whistling just wide of the post.
Sevilla's first chance of the night arrived in the 14th minute when Muriel robbed Samuel Umtiti of the ball before looking to pick out the top corner, but the striker's effort flashed wide of Marc-Andre ter Stegen's goal.
Andres Iniesta then sent one just wide of the Sevilla post in the 18th minute as the match somehow stayed level.
Barcelona finally made the breakthrough in the 23rd minute, however, when Alcacer took advantage of a terrible mistake from Sergio Escudero, who took a heavy touch in a dangerous position, before sliding the ball into the bottom corner.
Sevilla grew into the contest after the first goal, with Muriel's pace causing problems in the final third of the field. The visitors were struggling to create opportunities though as Barcelona entered the half-time break with a 1-0 lead.
It was Sevilla that had the first chance of the second period after Muriel found some space just outside the Barcelona box, but the 26-year-old sent his effort just over the crossbar.
Eduardo Berizzo's side were enjoying plenty of the ball as the match approached its hour mark, and should have levelled when Muriel found Pablo Sarabia unmarked inside the Barcelona box, but Nelson Semedo was across to make a last-ditch challenge.
Sevilla did equalise from the resulting set piece, however, as a brilliant header from Guido Pizarro ended up in the bottom corner of the net.
Barcelona came close to regaining their lead three minutes later when Pique released a powerful strike from outside the Sevilla box, but the centre-back's effort crashed off the crossbar.
The hosts did score their second in the 65th minute though when Alcacer converted a Rakitic cross from close range after Sevilla went to sleep at the back.
Soria made a smart save to prevent Messi from making it 3-1 Barcelona in the 72nd minute of action, and Sevilla were still very much in the argument approaching the final 15 minutes at Camp Nou.
Ter Stegen got down to keep out an Ever Banega strike in the 79th minute, but the visitors could not find a second as they lost their fourth league game of the season - allowing Barcelona to continue their stunning start to the 2017-18 campaign in the process.